Accession Number : AD0646926

Title :   A GENERALIZATION OF THE MOTZKIN THEOREM,

Corporate Author : PARKE MATHEMATICAL LABS INC CARLISLE MASS

Personal Author(s) : Calabi,Lorenzo ; Harnett,William E.

Report Date : NOV 1966

Pagination or Media Count : 32

Abstract : A figure A in the Euclidean plane is a compact set whose closed convex hull C(A) has a non empty interior; a ball of support for A is a closed ball which has points of A on the boundary but not in the interior. For each figure A, let C(A)-A denote the convex deficiency of A and let (S,q) denote the skeletal pair of A where S is the set of centers of maximal balls of support for A and q(x) is the distance from x to A for xeS. The following statements are proved: (1) Two figures have equal convex deficiencies if they have equal skeletal pairs. (2) (Motzkin's Theorem) A figure is convex if its skeleton is empty. (3) A figure is uniquely determined by its closed convex hull and its skeletal pair. (4) A figure with empty interior is uniquely determined by its skeletal pair. (Author)

Descriptors :   (*THEOREMS, *PATTERN RECOGNITION), (*MATHEMATICAL MODELS, *VISUAL PERCEPTION), CONVEX SETS, CONVEX BODIES, TOPOLOGY, MAPPING(TRANSFORMATIONS)

Subject Categories : Anatomy and Physiology
      Operations Research
      Bionics

Distribution Statement : APPROVED FOR PUBLIC RELEASE